My mum is wanting to take my son from leeds airport to southampton, we've established that he doesnt need a

passport but as im not accompanying them does he need some sort of permission letter from me?
hes 4 years old

they are travelling by plane, from leeds to southampton.
he wont needa passport because you dont need one travelling by plane inside uk.
he just needs an adult to vouch for him, BUT do i need to give some sort of written permission for him to be on the plane with him?

I assume from your question that they are travelling by public roads or transport, if that's the case your Mum doesn't need a letter from you, legally, however why not give her a letter of authorisation just in case she's stopped for whatever reason. It would save a lot of distress for you all if any authority had a doubt as to her right to be in charge of your son. If she's collecting your son from a flight at Leeds airport she will definitely need a written authorisation from you. I suggest attaching a copy of your passport/driving licence to the letter.